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A233256
T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs)
13
1, 1, 3, 3, 10, 11, 10, 104, 136, 48, 36, 1184, 4672, 2080, 236, 136, 13952, 166400, 221696, 32896, 1248, 528, 166400, 6049792, 23896064, 10620928, 524800, 6896, 2080, 1992704, 220626944, 2647261184, 3439984640, 509640704, 8390656, 39168, 8256
OFFSET
1,3
COMMENTS
Table starts
.......1...........1................3....................10
.......3..........10..............104..................1184
......11.........136.............4672................166400
......48........2080...........221696..............23896064
.....236.......32896.........10620928............3439984640
....1248......524800........509640704..........495341010944
....6896.....8390656......24461443072........71328837140480
...39168...134225920....1174138781696.....10271348253261824
..226496..2147516416...56358577635328...1479074079750225920
.1325568.34359869440.2705211055407104.212986666384520904704
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 12*a(n-1) -44*a(n-2) +48*a(n-3)
k=2: a(n) = 20*a(n-1) -64*a(n-2)
k=3: a(n) = 56*a(n-1) -384*a(n-2)
k=4: a(n) = 160*a(n-1) -2304*a(n-2)
k=5: a(n) = 512*a(n-1) -33792*a(n-2) +589824*a(n-3)
k=6: a(n) = 1664*a(n-1) -471040*a(n-2) +44826624*a(n-3) -1358954496*a(n-4)
k=7: [order 5]
Empirical for row n:
n=1: a(n) = 6*a(n-1) -8*a(n-2) for n>3
n=2: a(n) = 16*a(n-1) -48*a(n-2) for n>3
n=3: a(n) = 48*a(n-1) -448*a(n-2) +1024*a(n-3) for n>5
n=4: a(n) = 160*a(n-1) -6144*a(n-2) +86016*a(n-3) -393216*a(n-4) for n>8
n=5: [order 7] for n>11
n=6: [order 10] for n>16
n=7: [order 28] for n>34
EXAMPLE
Some solutions for n=3 k=4
..0..1..0..2....0..1..0..2....0..1..2..4....0..1..0..2....0..1..2..4
..5..3..5..2....2..1..0..4....3..4..2..4....3..4..0..4....2..0..3..1
..4..3..1..5....5..2..0..3....3..1..5..4....3..1..5..1....4..0..2..0
CROSSREFS
Column 1 is A233162(n+1)
Column 2 is A026244(n-1)
Row 1 is A007582(n-2)
Sequence in context: A124630 A321397 A128015 * A332955 A355089 A218953
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 06 2013
STATUS
approved